2x+26=4/11x

Solution for 2x+26=4/11x equation:

2x+26=4/11x

We move all terms to the left:

2x+26-(4/11x)=0


Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4/11x)+26=0

We get rid of parentheses

2x-4/11x+26=0

We multiply all the terms by the denominator


2x*11x+26*11x-4=0

Wy multiply elements

22x^2+286x-4=0

a = 22; b = 286; c = -4;
Δ = b2-4ac
Δ = 2862-4·22·(-4)
Δ = 82148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{82148}=\sqrt{4*20537}=\sqrt{4}*\sqrt{20537}=2\sqrt{20537}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(286)-2\sqrt{20537}}{2*22}=\frac{-286-2\sqrt{20537}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(286)+2\sqrt{20537}}{2*22}=\frac{-286+2\sqrt{20537}}{44}
$